[] add metering mode to CLI

1 files changed, 1796 insertions, 0 deletions

diff --git a/contrib/libs/clapack/dgesvj.c b/contrib/libs/clapack/dgesvj.c
new file mode 100644
index 0000000000..2d36977c0e
--- /dev/null
+++ b/contrib/libs/clapack/dgesvj.c
@@ -0,0 +1,1796 @@
+/* dgesvj.f -- translated by f2c (version 20061008).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static doublereal c_b17 = 0.;
+static doublereal c_b18 = 1.;
+static integer c__1 = 1;
+static integer c__0 = 0;
+static integer c__2 = 2;
+
+/* Subroutine */ int dgesvj_(char *joba, char *jobu, char *jobv, integer *m, 
+	integer *n, doublereal *a, integer *lda, doublereal *sva, integer *mv, 
+	 doublereal *v, integer *ldv, doublereal *work, integer *lwork, 
+	integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5;
+    doublereal d__1, d__2;
+
+    /* Builtin functions */
+    double sqrt(doublereal), d_sign(doublereal *, doublereal *);
+
+    /* Local variables */
+    doublereal bigtheta;
+    integer pskipped, i__, p, q;
+    doublereal t;
+    integer n2, n4;
+    doublereal rootsfmin;
+    integer n34;
+    doublereal cs, sn;
+    integer ir1, jbc;
+    doublereal big;
+    integer kbl, igl, ibr, jgl, nbl;
+    doublereal tol;
+    integer mvl;
+    doublereal aapp, aapq, aaqq;
+    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
+	    integer *);
+    doublereal ctol;
+    integer ierr;
+    doublereal aapp0;
+    extern doublereal dnrm2_(integer *, doublereal *, integer *);
+    doublereal temp1;
+    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
+	    integer *);
+    doublereal scale, large, apoaq, aqoap;
+    extern logical lsame_(char *, char *);
+    doublereal theta, small, sfmin;
+    logical lsvec;
+    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
+	    doublereal *, integer *);
+    doublereal fastr[5];
+    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
+	    doublereal *, integer *);
+    logical applv, rsvec;
+    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
+	    integer *, doublereal *, integer *);
+    logical uctol;
+    extern /* Subroutine */ int drotm_(integer *, doublereal *, integer *, 
+	    doublereal *, integer *, doublereal *);
+    logical lower, upper, rotok;
+    extern /* Subroutine */ int dgsvj0_(char *, integer *, integer *, 
+	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
+	    doublereal *, integer *, doublereal *, doublereal *, doublereal *, 
+	     integer *, doublereal *, integer *, integer *), dgsvj1_(
+	    char *, integer *, integer *, integer *, doublereal *, integer *, 
+	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
+	    doublereal *, doublereal *, doublereal *, integer *, doublereal *, 
+	     integer *, integer *);
+    extern doublereal dlamch_(char *);
+    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
+	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
+	    integer *, integer *);
+    extern integer idamax_(integer *, doublereal *, integer *);
+    extern /* Subroutine */ int dlaset_(char *, integer *, integer *, 
+	    doublereal *, doublereal *, doublereal *, integer *), 
+	    xerbla_(char *, integer *);
+    integer ijblsk, swband, blskip;
+    doublereal mxaapq;
+    extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, 
+	    doublereal *, doublereal *);
+    doublereal thsign, mxsinj;
+    integer emptsw, notrot, iswrot, lkahead;
+    logical goscale, noscale;
+    doublereal rootbig, epsilon, rooteps;
+    integer rowskip;
+    doublereal roottol;
+
+
+/*  -- LAPACK routine (version 3.2)                                    -- */
+
+/*  -- Contributed by Zlatko Drmac of the University of Zagreb and     -- */
+/*  -- Kresimir Veselic of the Fernuniversitaet Hagen                  -- */
+/*  -- November 2008                                                   -- */
+
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* This routine is also part of SIGMA (version 1.23, October 23. 2008.) */
+/* SIGMA is a library of algorithms for highly accurate algorithms for */
+/* computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the */
+/* eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. */
+
+/*     -#- Scalar Arguments -#- */
+
+
+/*     -#- Array Arguments -#- */
+
+/*     .. */
+
+/*  Purpose */
+/*  ~~~~~~~ */
+/*  DGESVJ computes the singular value decomposition (SVD) of a real */
+/*  M-by-N matrix A, where M >= N. The SVD of A is written as */
+/*                                     [++]   [xx]   [x0]   [xx] */
+/*               A = U * SIGMA * V^t,  [++] = [xx] * [ox] * [xx] */
+/*                                     [++]   [xx] */
+/*  where SIGMA is an N-by-N diagonal matrix, U is an M-by-N orthonormal */
+/*  matrix, and V is an N-by-N orthogonal matrix. The diagonal elements */
+/*  of SIGMA are the singular values of A. The columns of U and V are the */
+/*  left and the right singular vectors of A, respectively. */
+
+/*  Further Details */
+/*  ~~~~~~~~~~~~~~~ */
+/*  The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane */
+/*  rotations. The rotations are implemented as fast scaled rotations of */
+/*  Anda and Park [1]. In the case of underflow of the Jacobi angle, a */
+/*  modified Jacobi transformation of Drmac [4] is used. Pivot strategy uses */
+/*  column interchanges of de Rijk [2]. The relative accuracy of the computed */
+/*  singular values and the accuracy of the computed singular vectors (in */
+/*  angle metric) is as guaranteed by the theory of Demmel and Veselic [3]. */
+/*  The condition number that determines the accuracy in the full rank case */
+/*  is essentially min_{D=diag} kappa(A*D), where kappa(.) is the */
+/*  spectral condition number. The best performance of this Jacobi SVD */
+/*  procedure is achieved if used in an  accelerated version of Drmac and */
+/*  Veselic [5,6], and it is the kernel routine in the SIGMA library [7]. */
+/*  Some tunning parameters (marked with [TP]) are available for the */
+/*  implementer. */
+/*  The computational range for the nonzero singular values is the  machine */
+/*  number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even */
+/*  denormalized singular values can be computed with the corresponding */
+/*  gradual loss of accurate digits. */
+
+/*  Contributors */
+/*  ~~~~~~~~~~~~ */
+/*  Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) */
+
+/*  References */
+/*  ~~~~~~~~~~ */
+/* [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling. */
+/*     SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174. */
+/* [2] P. P. M. De Rijk: A one-sided Jacobi algorithm for computing the */
+/*     singular value decomposition on a vector computer. */
+/*     SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371. */
+/* [3] J. Demmel and K. Veselic: Jacobi method is more accurate than QR. */
+/* [4] Z. Drmac: Implementation of Jacobi rotations for accurate singular */
+/*     value computation in floating point arithmetic. */
+/*     SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222. */
+/* [5] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I. */
+/*     SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342. */
+/*     LAPACK Working note 169. */
+/* [6] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II. */
+/*     SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362. */
+/*     LAPACK Working note 170. */
+/* [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV, */
+/*     QSVD, (H,K)-SVD computations. */
+/*     Department of Mathematics, University of Zagreb, 2008. */
+
+/*  Bugs, Examples and Comments */
+/*  ~~~~~~~~~~~~~~~~~~~~~~~~~~~ */
+/*  Please report all bugs and send interesting test examples and comments to */
+/*  drmac@math.hr. Thank you. */
+
+/*  Arguments */
+/*  ~~~~~~~~~ */
+
+/*  JOBA    (input) CHARACTER* 1 */
+/*          Specifies the structure of A. */
+/*          = 'L': The input matrix A is lower triangular; */
+/*          = 'U': The input matrix A is upper triangular; */
+/*          = 'G': The input matrix A is general M-by-N matrix, M >= N. */
+
+/*  JOBU    (input) CHARACTER*1 */
+/*          Specifies whether to compute the left singular vectors */
+/*          (columns of U): */
+
+/*          = 'U': The left singular vectors corresponding to the nonzero */
+/*                 singular values are computed and returned in the leading */
+/*                 columns of A. See more details in the description of A. */
+/*                 The default numerical orthogonality threshold is set to */
+/*                 approximately TOL=CTOL*EPS, CTOL=DSQRT(M), EPS=DLAMCH('E'). */
+/*          = 'C': Analogous to JOBU='U', except that user can control the */
+/*                 level of numerical orthogonality of the computed left */
+/*                 singular vectors. TOL can be set to TOL = CTOL*EPS, where */
+/*                 CTOL is given on input in the array WORK. */
+/*                 No CTOL smaller than ONE is allowed. CTOL greater */
+/*                 than 1 / EPS is meaningless. The option 'C' */
+/*                 can be used if M*EPS is satisfactory orthogonality */
+/*                 of the computed left singular vectors, so CTOL=M could */
+/*                 save few sweeps of Jacobi rotations. */
+/*                 See the descriptions of A and WORK(1). */
+/*          = 'N': The matrix U is not computed. However, see the */
+/*                 description of A. */
+
+/*  JOBV    (input) CHARACTER*1 */
+/*          Specifies whether to compute the right singular vectors, that */
+/*          is, the matrix V: */
+/*          = 'V' : the matrix V is computed and returned in the array V */
+/*          = 'A' : the Jacobi rotations are applied to the MV-by-N */
+/*                  array V. In other words, the right singular vector */
+/*                  matrix V is not computed explicitly, instead it is */
+/*                  applied to an MV-by-N matrix initially stored in the */
+/*                  first MV rows of V. */
+/*          = 'N' : the matrix V is not computed and the array V is not */
+/*                  referenced */
+
+/*  M       (input) INTEGER */
+/*          The number of rows of the input matrix A.  M >= 0. */
+
+/*  N       (input) INTEGER */
+/*          The number of columns of the input matrix A. */
+/*          M >= N >= 0. */
+
+/*  A       (input/output) REAL array, dimension (LDA,N) */
+/*          On entry, the M-by-N matrix A. */
+/*          On exit, */
+/*          If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C': */
+/*          ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */
+/*                 If INFO .EQ. 0, */
+/*                 ~~~~~~~~~~~~~~~ */
+/*                 RANKA orthonormal columns of U are returned in the */
+/*                 leading RANKA columns of the array A. Here RANKA <= N */
+/*                 is the number of computed singular values of A that are */
+/*                 above the underflow threshold DLAMCH('S'). The singular */
+/*                 vectors corresponding to underflowed or zero singular */
+/*                 values are not computed. The value of RANKA is returned */
+/*                 in the array WORK as RANKA=NINT(WORK(2)). Also see the */
+/*                 descriptions of SVA and WORK. The computed columns of U */
+/*                 are mutually numerically orthogonal up to approximately */
+/*                 TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'), */
+/*                 see the description of JOBU. */
+/*                 If INFO .GT. 0, */
+/*                 ~~~~~~~~~~~~~~~ */
+/*                 the procedure DGESVJ did not converge in the given number */
+/*                 of iterations (sweeps). In that case, the computed */
+/*                 columns of U may not be orthogonal up to TOL. The output */
+/*                 U (stored in A), SIGMA (given by the computed singular */
+/*                 values in SVA(1:N)) and V is still a decomposition of the */
+/*                 input matrix A in the sense that the residual */
+/*                 ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small. */
+
+/*          If JOBU .EQ. 'N': */
+/*          ~~~~~~~~~~~~~~~~~ */
+/*                 If INFO .EQ. 0 */
+/*                 ~~~~~~~~~~~~~~ */
+/*                 Note that the left singular vectors are 'for free' in the */
+/*                 one-sided Jacobi SVD algorithm. However, if only the */
+/*                 singular values are needed, the level of numerical */
+/*                 orthogonality of U is not an issue and iterations are */
+/*                 stopped when the columns of the iterated matrix are */
+/*                 numerically orthogonal up to approximately M*EPS. Thus, */
+/*                 on exit, A contains the columns of U scaled with the */
+/*                 corresponding singular values. */
+/*                 If INFO .GT. 0, */
+/*                 ~~~~~~~~~~~~~~~ */
+/*                 the procedure DGESVJ did not converge in the given number */
+/*                 of iterations (sweeps). */
+
+/*  LDA     (input) INTEGER */
+/*          The leading dimension of the array A.  LDA >= max(1,M). */
+
+/*  SVA     (workspace/output) REAL array, dimension (N) */
+/*          On exit, */
+/*          If INFO .EQ. 0, */
+/*          ~~~~~~~~~~~~~~~ */
+/*          depending on the value SCALE = WORK(1), we have: */
+/*                 If SCALE .EQ. ONE: */
+/*                 ~~~~~~~~~~~~~~~~~~ */
+/*                 SVA(1:N) contains the computed singular values of A. */
+/*                 During the computation SVA contains the Euclidean column */
+/*                 norms of the iterated matrices in the array A. */
+/*                 If SCALE .NE. ONE: */
+/*                 ~~~~~~~~~~~~~~~~~~ */
+/*                 The singular values of A are SCALE*SVA(1:N), and this */
+/*                 factored representation is due to the fact that some of the */
+/*                 singular values of A might underflow or overflow. */
+
+/*          If INFO .GT. 0, */
+/*          ~~~~~~~~~~~~~~~ */
+/*          the procedure DGESVJ did not converge in the given number of */
+/*          iterations (sweeps) and SCALE*SVA(1:N) may not be accurate. */
+
+/*  MV      (input) INTEGER */
+/*          If JOBV .EQ. 'A', then the product of Jacobi rotations in DGESVJ */
+/*          is applied to the first MV rows of V. See the description of JOBV. */
+
+/*  V       (input/output) REAL array, dimension (LDV,N) */
+/*          If JOBV = 'V', then V contains on exit the N-by-N matrix of */
+/*                         the right singular vectors; */
+/*          If JOBV = 'A', then V contains the product of the computed right */
+/*                         singular vector matrix and the initial matrix in */
+/*                         the array V. */
+/*          If JOBV = 'N', then V is not referenced. */
+
+/*  LDV     (input) INTEGER */
+/*          The leading dimension of the array V, LDV .GE. 1. */
+/*          If JOBV .EQ. 'V', then LDV .GE. max(1,N). */
+/*          If JOBV .EQ. 'A', then LDV .GE. max(1,MV) . */
+
+/*  WORK    (input/workspace/output) REAL array, dimension max(4,M+N). */
+/*          On entry, */
+/*          If JOBU .EQ. 'C', */
+/*          ~~~~~~~~~~~~~~~~~ */
+/*          WORK(1) = CTOL, where CTOL defines the threshold for convergence. */
+/*                    The process stops if all columns of A are mutually */
+/*                    orthogonal up to CTOL*EPS, EPS=DLAMCH('E'). */
+/*                    It is required that CTOL >= ONE, i.e. it is not */
+/*                    allowed to force the routine to obtain orthogonality */
+/*                    below EPSILON. */
+/*          On exit, */
+/*          WORK(1) = SCALE is the scaling factor such that SCALE*SVA(1:N) */
+/*                    are the computed singular vcalues of A. */
+/*                    (See description of SVA().) */
+/*          WORK(2) = NINT(WORK(2)) is the number of the computed nonzero */
+/*                    singular values. */
+/*          WORK(3) = NINT(WORK(3)) is the number of the computed singular */
+/*                    values that are larger than the underflow threshold. */
+/*          WORK(4) = NINT(WORK(4)) is the number of sweeps of Jacobi */
+/*                    rotations needed for numerical convergence. */
+/*          WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep. */
+/*                    This is useful information in cases when DGESVJ did */
+/*                    not converge, as it can be used to estimate whether */
+/*                    the output is stil useful and for post festum analysis. */
+/*          WORK(6) = the largest absolute value over all sines of the */
+/*                    Jacobi rotation angles in the last sweep. It can be */
+/*                    useful for a post festum analysis. */
+
+/*  LWORK   length of WORK, WORK >= MAX(6,M+N) */
+
+/*  INFO    (output) INTEGER */
+/*          = 0 : successful exit. */
+/*          < 0 : if INFO = -i, then the i-th argument had an illegal value */
+/*          > 0 : DGESVJ did not converge in the maximal allowed number (30) */
+/*                of sweeps. The output may still be useful. See the */
+/*                description of WORK. */
+
+/*     Local Parameters */
+
+
+/*     Local Scalars */
+
+
+/*     Local Arrays */
+
+
+/*     Intrinsic Functions */
+
+
+/*     External Functions */
+/*     .. from BLAS */
+/*     .. from LAPACK */
+
+/*     External Subroutines */
+/*     .. from BLAS */
+/*     .. from LAPACK */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    --sva;
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    v_dim1 = *ldv;
+    v_offset = 1 + v_dim1;
+    v -= v_offset;
+    --work;
+
+    /* Function Body */
+    lsvec = lsame_(jobu, "U");
+    uctol = lsame_(jobu, "C");
+    rsvec = lsame_(jobv, "V");
+    applv = lsame_(jobv, "A");
+    upper = lsame_(joba, "U");
+    lower = lsame_(joba, "L");
+
+    if (! (upper || lower || lsame_(joba, "G"))) {
+	*info = -1;
+    } else if (! (lsvec || uctol || lsame_(jobu, "N"))) 
+	    {
+	*info = -2;
+    } else if (! (rsvec || applv || lsame_(jobv, "N"))) 
+	    {
+	*info = -3;
+    } else if (*m < 0) {
+	*info = -4;
+    } else if (*n < 0 || *n > *m) {
+	*info = -5;
+    } else if (*lda < *m) {
+	*info = -7;
+    } else if (*mv < 0) {
+	*info = -9;
+    } else if (rsvec && *ldv < *n || applv && *ldv < *mv) {
+	*info = -11;
+    } else if (uctol && work[1] <= 1.) {
+	*info = -12;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = *m + *n;
+	if (*lwork < max(i__1,6)) {
+	    *info = -13;
+	} else {
+	    *info = 0;
+	}
+    }
+
+/*     #:( */
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DGESVJ", &i__1);
+	return 0;
+    }
+
+/* #:) Quick return for void matrix */
+
+    if (*m == 0 || *n == 0) {
+	return 0;
+    }
+
+/*     Set numerical parameters */
+/*     The stopping criterion for Jacobi rotations is */
+
+/*     max_{i<>j}|A(:,i)^T * A(:,j)|/(||A(:,i)||*||A(:,j)||) < CTOL*EPS */
+
+/*     where EPS is the round-off and CTOL is defined as follows: */
+
+    if (uctol) {
+/*        ... user controlled */
+	ctol = work[1];
+    } else {
+/*        ... default */
+	if (lsvec || rsvec || applv) {
+	    ctol = sqrt((doublereal) (*m));
+	} else {
+	    ctol = (doublereal) (*m);
+	}
+    }
+/*     ... and the machine dependent parameters are */
+/* [!]  (Make sure that DLAMCH() works properly on the target machine.) */
+
+    epsilon = dlamch_("Epsilon");
+    rooteps = sqrt(epsilon);
+    sfmin = dlamch_("SafeMinimum");
+    rootsfmin = sqrt(sfmin);
+    small = sfmin / epsilon;
+    big = dlamch_("Overflow");
+/*     BIG         = ONE    / SFMIN */
+    rootbig = 1. / rootsfmin;
+    large = big / sqrt((doublereal) (*m * *n));
+    bigtheta = 1. / rooteps;
+
+    tol = ctol * epsilon;
+    roottol = sqrt(tol);
+
+    if ((doublereal) (*m) * epsilon >= 1.) {
+	*info = -5;
+	i__1 = -(*info);
+	xerbla_("DGESVJ", &i__1);
+	return 0;
+    }
+
+/*     Initialize the right singular vector matrix. */
+
+    if (rsvec) {
+	mvl = *n;
+	dlaset_("A", &mvl, n, &c_b17, &c_b18, &v[v_offset], ldv);
+    } else if (applv) {
+	mvl = *mv;
+    }
+    rsvec = rsvec || applv;
+
+/*     Initialize SVA( 1:N ) = ( ||A e_i||_2, i = 1:N ) */
+/* (!)  If necessary, scale A to protect the largest singular value */
+/*     from overflow. It is possible that saving the largest singular */
+/*     value destroys the information about the small ones. */
+/*     This initial scaling is almost minimal in the sense that the */
+/*     goal is to make sure that no column norm overflows, and that */
+/*     DSQRT(N)*max_i SVA(i) does not overflow. If INFinite entries */
+/*     in A are detected, the procedure returns with INFO=-6. */
+
+    scale = 1. / sqrt((doublereal) (*m) * (doublereal) (*n));
+    noscale = TRUE_;
+    goscale = TRUE_;
+
+    if (lower) {
+/*        the input matrix is M-by-N lower triangular (trapezoidal) */
+	i__1 = *n;
+	for (p = 1; p <= i__1; ++p) {
+	    aapp = 0.;
+	    aaqq = 0.;
+	    i__2 = *m - p + 1;
+	    dlassq_(&i__2, &a[p + p * a_dim1], &c__1, &aapp, &aaqq);
+	    if (aapp > big) {
+		*info = -6;
+		i__2 = -(*info);
+		xerbla_("DGESVJ", &i__2);
+		return 0;
+	    }
+	    aaqq = sqrt(aaqq);
+	    if (aapp < big / aaqq && noscale) {
+		sva[p] = aapp * aaqq;
+	    } else {
+		noscale = FALSE_;
+		sva[p] = aapp * (aaqq * scale);
+		if (goscale) {
+		    goscale = FALSE_;
+		    i__2 = p - 1;
+		    for (q = 1; q <= i__2; ++q) {
+			sva[q] *= scale;
+/* L1873: */
+		    }
+		}
+	    }
+/* L1874: */
+	}
+    } else if (upper) {
+/*        the input matrix is M-by-N upper triangular (trapezoidal) */
+	i__1 = *n;
+	for (p = 1; p <= i__1; ++p) {
+	    aapp = 0.;
+	    aaqq = 0.;
+	    dlassq_(&p, &a[p * a_dim1 + 1], &c__1, &aapp, &aaqq);
+	    if (aapp > big) {
+		*info = -6;
+		i__2 = -(*info);
+		xerbla_("DGESVJ", &i__2);
+		return 0;
+	    }
+	    aaqq = sqrt(aaqq);
+	    if (aapp < big / aaqq && noscale) {
+		sva[p] = aapp * aaqq;
+	    } else {
+		noscale = FALSE_;
+		sva[p] = aapp * (aaqq * scale);
+		if (goscale) {
+		    goscale = FALSE_;
+		    i__2 = p - 1;
+		    for (q = 1; q <= i__2; ++q) {
+			sva[q] *= scale;
+/* L2873: */
+		    }
+		}
+	    }
+/* L2874: */
+	}
+    } else {
+/*        the input matrix is M-by-N general dense */
+	i__1 = *n;
+	for (p = 1; p <= i__1; ++p) {
+	    aapp = 0.;
+	    aaqq = 0.;
+	    dlassq_(m, &a[p * a_dim1 + 1], &c__1, &aapp, &aaqq);
+	    if (aapp > big) {
+		*info = -6;
+		i__2 = -(*info);
+		xerbla_("DGESVJ", &i__2);
+		return 0;
+	    }
+	    aaqq = sqrt(aaqq);
+	    if (aapp < big / aaqq && noscale) {
+		sva[p] = aapp * aaqq;
+	    } else {
+		noscale = FALSE_;
+		sva[p] = aapp * (aaqq * scale);
+		if (goscale) {
+		    goscale = FALSE_;
+		    i__2 = p - 1;
+		    for (q = 1; q <= i__2; ++q) {
+			sva[q] *= scale;
+/* L3873: */
+		    }
+		}
+	    }
+/* L3874: */
+	}
+    }
+
+    if (noscale) {
+	scale = 1.;
+    }
+
+/*     Move the smaller part of the spectrum from the underflow threshold */
+/* (!)  Start by determining the position of the nonzero entries of the */
+/*     array SVA() relative to ( SFMIN, BIG ). */
+
+    aapp = 0.;
+    aaqq = big;
+    i__1 = *n;
+    for (p = 1; p <= i__1; ++p) {
+	if (sva[p] != 0.) {
+/* Computing MIN */
+	    d__1 = aaqq, d__2 = sva[p];
+	    aaqq = min(d__1,d__2);
+	}
+/* Computing MAX */
+	d__1 = aapp, d__2 = sva[p];
+	aapp = max(d__1,d__2);
+/* L4781: */
+    }
+
+/* #:) Quick return for zero matrix */
+
+    if (aapp == 0.) {
+	if (lsvec) {
+	    dlaset_("G", m, n, &c_b17, &c_b18, &a[a_offset], lda);
+	}
+	work[1] = 1.;
+	work[2] = 0.;
+	work[3] = 0.;
+	work[4] = 0.;
+	work[5] = 0.;
+	work[6] = 0.;
+	return 0;
+    }
+
+/* #:) Quick return for one-column matrix */
+
+    if (*n == 1) {
+	if (lsvec) {
+	    dlascl_("G", &c__0, &c__0, &sva[1], &scale, m, &c__1, &a[a_dim1 + 
+		    1], lda, &ierr);
+	}
+	work[1] = 1. / scale;
+	if (sva[1] >= sfmin) {
+	    work[2] = 1.;
+	} else {
+	    work[2] = 0.;
+	}
+	work[3] = 0.;
+	work[4] = 0.;
+	work[5] = 0.;
+	work[6] = 0.;
+	return 0;
+    }
+
+/*     Protect small singular values from underflow, and try to */
+/*     avoid underflows/overflows in computing Jacobi rotations. */
+
+    sn = sqrt(sfmin / epsilon);
+    temp1 = sqrt(big / (doublereal) (*n));
+    if (aapp <= sn || aaqq >= temp1 || sn <= aaqq && aapp <= temp1) {
+/* Computing MIN */
+	d__1 = big, d__2 = temp1 / aapp;
+	temp1 = min(d__1,d__2);
+/*         AAQQ  = AAQQ*TEMP1 */
+/*         AAPP  = AAPP*TEMP1 */
+    } else if (aaqq <= sn && aapp <= temp1) {
+/* Computing MIN */
+	d__1 = sn / aaqq, d__2 = big / (aapp * sqrt((doublereal) (*n)));
+	temp1 = min(d__1,d__2);
+/*         AAQQ  = AAQQ*TEMP1 */
+/*         AAPP  = AAPP*TEMP1 */
+    } else if (aaqq >= sn && aapp >= temp1) {
+/* Computing MAX */
+	d__1 = sn / aaqq, d__2 = temp1 / aapp;
+	temp1 = max(d__1,d__2);
+/*         AAQQ  = AAQQ*TEMP1 */
+/*         AAPP  = AAPP*TEMP1 */
+    } else if (aaqq <= sn && aapp >= temp1) {
+/* Computing MIN */
+	d__1 = sn / aaqq, d__2 = big / (sqrt((doublereal) (*n)) * aapp);
+	temp1 = min(d__1,d__2);
+/*         AAQQ  = AAQQ*TEMP1 */
+/*         AAPP  = AAPP*TEMP1 */
+    } else {
+	temp1 = 1.;
+    }
+
+/*     Scale, if necessary */
+
+    if (temp1 != 1.) {
+	dlascl_("G", &c__0, &c__0, &c_b18, &temp1, n, &c__1, &sva[1], n, &
+		ierr);
+    }
+    scale = temp1 * scale;
+    if (scale != 1.) {
+	dlascl_(joba, &c__0, &c__0, &c_b18, &scale, m, n, &a[a_offset], lda, &
+		ierr);
+	scale = 1. / scale;
+    }
+
+/*     Row-cyclic Jacobi SVD algorithm with column pivoting */
+
+    emptsw = *n * (*n - 1) / 2;
+    notrot = 0;
+    fastr[0] = 0.;
+
+/*     A is represented in factored form A = A * diag(WORK), where diag(WORK) */
+/*     is initialized to identity. WORK is updated during fast scaled */
+/*     rotations. */
+
+    i__1 = *n;
+    for (q = 1; q <= i__1; ++q) {
+	work[q] = 1.;
+/* L1868: */
+    }
+
+
+    swband = 3;
+/* [TP] SWBAND is a tuning parameter [TP]. It is meaningful and effective */
+/*     if DGESVJ is used as a computational routine in the preconditioned */
+/*     Jacobi SVD algorithm DGESVJ. For sweeps i=1:SWBAND the procedure */
+/*     works on pivots inside a band-like region around the diagonal. */
+/*     The boundaries are determined dynamically, based on the number of */
+/*     pivots above a threshold. */
+
+    kbl = min(8,*n);
+/* [TP] KBL is a tuning parameter that defines the tile size in the */
+/*     tiling of the p-q loops of pivot pairs. In general, an optimal */
+/*     value of KBL depends on the matrix dimensions and on the */
+/*     parameters of the computer's memory. */
+
+    nbl = *n / kbl;
+    if (nbl * kbl != *n) {
+	++nbl;
+    }
+
+/* Computing 2nd power */
+    i__1 = kbl;
+    blskip = i__1 * i__1;
+/* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */
+
+    rowskip = min(5,kbl);
+/* [TP] ROWSKIP is a tuning parameter. */
+
+    lkahead = 1;
+/* [TP] LKAHEAD is a tuning parameter. */
+
+/*     Quasi block transformations, using the lower (upper) triangular */
+/*     structure of the input matrix. The quasi-block-cycling usually */
+/*     invokes cubic convergence. Big part of this cycle is done inside */
+/*     canonical subspaces of dimensions less than M. */
+
+/* Computing MAX */
+    i__1 = 64, i__2 = kbl << 2;
+    if ((lower || upper) && *n > max(i__1,i__2)) {
+/* [TP] The number of partition levels and the actual partition are */
+/*     tuning parameters. */
+	n4 = *n / 4;
+	n2 = *n / 2;
+	n34 = n4 * 3;
+	if (applv) {
+	    q = 0;
+	} else {
+	    q = 1;
+	}
+
+	if (lower) {
+
+/*     This works very well on lower triangular matrices, in particular */
+/*     in the framework of the preconditioned Jacobi SVD (xGEJSV). */
+/*     The idea is simple: */
+/*     [+ 0 0 0]   Note that Jacobi transformations of [0 0] */
+/*     [+ + 0 0]                                       [0 0] */
+/*     [+ + x 0]   actually work on [x 0]              [x 0] */
+/*     [+ + x x]                    [x x].             [x x] */
+
+	    i__1 = *m - n34;
+	    i__2 = *n - n34;
+	    i__3 = *lwork - *n;
+	    dgsvj0_(jobv, &i__1, &i__2, &a[n34 + 1 + (n34 + 1) * a_dim1], lda, 
+		     &work[n34 + 1], &sva[n34 + 1], &mvl, &v[n34 * q + 1 + (
+		    n34 + 1) * v_dim1], ldv, &epsilon, &sfmin, &tol, &c__2, &
+		    work[*n + 1], &i__3, &ierr);
+
+	    i__1 = *m - n2;
+	    i__2 = n34 - n2;
+	    i__3 = *lwork - *n;
+	    dgsvj0_(jobv, &i__1, &i__2, &a[n2 + 1 + (n2 + 1) * a_dim1], lda, &
+		    work[n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (n2 + 1)
+		     * v_dim1], ldv, &epsilon, &sfmin, &tol, &c__2, &work[*n 
+		    + 1], &i__3, &ierr);
+
+	    i__1 = *m - n2;
+	    i__2 = *n - n2;
+	    i__3 = *lwork - *n;
+	    dgsvj1_(jobv, &i__1, &i__2, &n4, &a[n2 + 1 + (n2 + 1) * a_dim1], 
+		    lda, &work[n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (
+		    n2 + 1) * v_dim1], ldv, &epsilon, &sfmin, &tol, &c__1, &
+		    work[*n + 1], &i__3, &ierr);
+
+	    i__1 = *m - n4;
+	    i__2 = n2 - n4;
+	    i__3 = *lwork - *n;
+	    dgsvj0_(jobv, &i__1, &i__2, &a[n4 + 1 + (n4 + 1) * a_dim1], lda, &
+		    work[n4 + 1], &sva[n4 + 1], &mvl, &v[n4 * q + 1 + (n4 + 1)
+		     * v_dim1], ldv, &epsilon, &sfmin, &tol, &c__1, &work[*n 
+		    + 1], &i__3, &ierr);
+
+	    i__1 = *lwork - *n;
+	    dgsvj0_(jobv, m, &n4, &a[a_offset], lda, &work[1], &sva[1], &mvl, 
+		    &v[v_offset], ldv, &epsilon, &sfmin, &tol, &c__1, &work[*
+		    n + 1], &i__1, &ierr);
+
+	    i__1 = *lwork - *n;
+	    dgsvj1_(jobv, m, &n2, &n4, &a[a_offset], lda, &work[1], &sva[1], &
+		    mvl, &v[v_offset], ldv, &epsilon, &sfmin, &tol, &c__1, &
+		    work[*n + 1], &i__1, &ierr);
+
+
+	} else if (upper) {
+
+
+	    i__1 = *lwork - *n;
+	    dgsvj0_(jobv, &n4, &n4, &a[a_offset], lda, &work[1], &sva[1], &
+		    mvl, &v[v_offset], ldv, &epsilon, &sfmin, &tol, &c__2, &
+		    work[*n + 1], &i__1, &ierr);
+
+	    i__1 = *lwork - *n;
+	    dgsvj0_(jobv, &n2, &n4, &a[(n4 + 1) * a_dim1 + 1], lda, &work[n4 
+		    + 1], &sva[n4 + 1], &mvl, &v[n4 * q + 1 + (n4 + 1) * 
+		    v_dim1], ldv, &epsilon, &sfmin, &tol, &c__1, &work[*n + 1]
+, &i__1, &ierr);
+
+	    i__1 = *lwork - *n;
+	    dgsvj1_(jobv, &n2, &n2, &n4, &a[a_offset], lda, &work[1], &sva[1], 
+		     &mvl, &v[v_offset], ldv, &epsilon, &sfmin, &tol, &c__1, &
+		    work[*n + 1], &i__1, &ierr);
+
+	    i__1 = n2 + n4;
+	    i__2 = *lwork - *n;
+	    dgsvj0_(jobv, &i__1, &n4, &a[(n2 + 1) * a_dim1 + 1], lda, &work[
+		    n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (n2 + 1) * 
+		    v_dim1], ldv, &epsilon, &sfmin, &tol, &c__1, &work[*n + 1]
+, &i__2, &ierr);
+	}
+
+    }
+
+/*     -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- */
+
+    for (i__ = 1; i__ <= 30; ++i__) {
+
+/*     .. go go go ... */
+
+	mxaapq = 0.;
+	mxsinj = 0.;
+	iswrot = 0;
+
+	notrot = 0;
+	pskipped = 0;
+
+/*     Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs */
+/*     1 <= p < q <= N. This is the first step toward a blocked implementation */
+/*     of the rotations. New implementation, based on block transformations, */
+/*     is under development. */
+
+	i__1 = nbl;
+	for (ibr = 1; ibr <= i__1; ++ibr) {
+
+	    igl = (ibr - 1) * kbl + 1;
+
+/* Computing MIN */
+	    i__3 = lkahead, i__4 = nbl - ibr;
+	    i__2 = min(i__3,i__4);
+	    for (ir1 = 0; ir1 <= i__2; ++ir1) {
+
+		igl += ir1 * kbl;
+
+/* Computing MIN */
+		i__4 = igl + kbl - 1, i__5 = *n - 1;
+		i__3 = min(i__4,i__5);
+		for (p = igl; p <= i__3; ++p) {
+
+/*     .. de Rijk's pivoting */
+
+		    i__4 = *n - p + 1;
+		    q = idamax_(&i__4, &sva[p], &c__1) + p - 1;
+		    if (p != q) {
+			dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 
+				1], &c__1);
+			if (rsvec) {
+			    dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * 
+				    v_dim1 + 1], &c__1);
+			}
+			temp1 = sva[p];
+			sva[p] = sva[q];
+			sva[q] = temp1;
+			temp1 = work[p];
+			work[p] = work[q];
+			work[q] = temp1;
+		    }
+
+		    if (ir1 == 0) {
+
+/*        Column norms are periodically updated by explicit */
+/*        norm computation. */
+/*        Caveat: */
+/*        Unfortunately, some BLAS implementations compute DNRM2(M,A(1,p),1) */
+/*        as DSQRT(DDOT(M,A(1,p),1,A(1,p),1)), which may cause the result to */
+/*        overflow for ||A(:,p)||_2 > DSQRT(overflow_threshold), and to */
+/*        underflow for ||A(:,p)||_2 < DSQRT(underflow_threshold). */
+/*        Hence, DNRM2 cannot be trusted, not even in the case when */
+/*        the true norm is far from the under(over)flow boundaries. */
+/*        If properly implemented DNRM2 is available, the IF-THEN-ELSE */
+/*        below should read "AAPP = DNRM2( M, A(1,p), 1 ) * WORK(p)". */
+
+			if (sva[p] < rootbig && sva[p] > rootsfmin) {
+			    sva[p] = dnrm2_(m, &a[p * a_dim1 + 1], &c__1) * 
+				    work[p];
+			} else {
+			    temp1 = 0.;
+			    aapp = 0.;
+			    dlassq_(m, &a[p * a_dim1 + 1], &c__1, &temp1, &
+				    aapp);
+			    sva[p] = temp1 * sqrt(aapp) * work[p];
+			}
+			aapp = sva[p];
+		    } else {
+			aapp = sva[p];
+		    }
+
+		    if (aapp > 0.) {
+
+			pskipped = 0;
+
+/* Computing MIN */
+			i__5 = igl + kbl - 1;
+			i__4 = min(i__5,*n);
+			for (q = p + 1; q <= i__4; ++q) {
+
+			    aaqq = sva[q];
+
+			    if (aaqq > 0.) {
+
+				aapp0 = aapp;
+				if (aaqq >= 1.) {
+				    rotok = small * aapp <= aaqq;
+				    if (aapp < big / aaqq) {
+					aapq = ddot_(m, &a[p * a_dim1 + 1], &
+						c__1, &a[q * a_dim1 + 1], &
+						c__1) * work[p] * work[q] / 
+						aaqq / aapp;
+				    } else {
+					dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
+						work[*n + 1], &c__1);
+					dlascl_("G", &c__0, &c__0, &aapp, &
+						work[p], m, &c__1, &work[*n + 
+						1], lda, &ierr);
+					aapq = ddot_(m, &work[*n + 1], &c__1, 
+						&a[q * a_dim1 + 1], &c__1) * 
+						work[q] / aaqq;
+				    }
+				} else {
+				    rotok = aapp <= aaqq / small;
+				    if (aapp > small / aaqq) {
+					aapq = ddot_(m, &a[p * a_dim1 + 1], &
+						c__1, &a[q * a_dim1 + 1], &
+						c__1) * work[p] * work[q] / 
+						aaqq / aapp;
+				    } else {
+					dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
+						work[*n + 1], &c__1);
+					dlascl_("G", &c__0, &c__0, &aaqq, &
+						work[q], m, &c__1, &work[*n + 
+						1], lda, &ierr);
+					aapq = ddot_(m, &work[*n + 1], &c__1, 
+						&a[p * a_dim1 + 1], &c__1) * 
+						work[p] / aapp;
+				    }
+				}
+
+/* Computing MAX */
+				d__1 = mxaapq, d__2 = abs(aapq);
+				mxaapq = max(d__1,d__2);
+
+/*        TO rotate or NOT to rotate, THAT is the question ... */
+
+				if (abs(aapq) > tol) {
+
+/*           .. rotate */
+/* [RTD]      ROTATED = ROTATED + ONE */
+
+				    if (ir1 == 0) {
+					notrot = 0;
+					pskipped = 0;
+					++iswrot;
+				    }
+
+				    if (rotok) {
+
+					aqoap = aaqq / aapp;
+					apoaq = aapp / aaqq;
+					theta = (d__1 = aqoap - apoaq, abs(
+						d__1)) * -.5 / aapq;
+
+					if (abs(theta) > bigtheta) {
+
+					    t = .5 / theta;
+					    fastr[2] = t * work[p] / work[q];
+					    fastr[3] = -t * work[q] / work[p];
+					    drotm_(m, &a[p * a_dim1 + 1], &
+						    c__1, &a[q * a_dim1 + 1], 
+						    &c__1, fastr);
+					    if (rsvec) {
+			  drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * 
+				  v_dim1 + 1], &c__1, fastr);
+					    }
+/* Computing MAX */
+					    d__1 = 0., d__2 = t * apoaq * 
+						    aapq + 1.;
+					    sva[q] = aaqq * sqrt((max(d__1,
+						    d__2)));
+					    aapp *= sqrt(1. - t * aqoap * 
+						    aapq);
+/* Computing MAX */
+					    d__1 = mxsinj, d__2 = abs(t);
+					    mxsinj = max(d__1,d__2);
+
+					} else {
+
+/*                 .. choose correct signum for THETA and rotate */
+
+					    thsign = -d_sign(&c_b18, &aapq);
+					    t = 1. / (theta + thsign * sqrt(
+						    theta * theta + 1.));
+					    cs = sqrt(1. / (t * t + 1.));
+					    sn = t * cs;
+
+/* Computing MAX */
+					    d__1 = mxsinj, d__2 = abs(sn);
+					    mxsinj = max(d__1,d__2);
+/* Computing MAX */
+					    d__1 = 0., d__2 = t * apoaq * 
+						    aapq + 1.;
+					    sva[q] = aaqq * sqrt((max(d__1,
+						    d__2)));
+/* Computing MAX */
+					    d__1 = 0., d__2 = 1. - t * aqoap *
+						     aapq;
+					    aapp *= sqrt((max(d__1,d__2)));
+
+					    apoaq = work[p] / work[q];
+					    aqoap = work[q] / work[p];
+					    if (work[p] >= 1.) {
+			  if (work[q] >= 1.) {
+			      fastr[2] = t * apoaq;
+			      fastr[3] = -t * aqoap;
+			      work[p] *= cs;
+			      work[q] *= cs;
+			      drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q * 
+				      a_dim1 + 1], &c__1, fastr);
+			      if (rsvec) {
+				  drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
+					  q * v_dim1 + 1], &c__1, fastr);
+			      }
+			  } else {
+			      d__1 = -t * aqoap;
+			      daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
+				      p * a_dim1 + 1], &c__1);
+			      d__1 = cs * sn * apoaq;
+			      daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
+				      q * a_dim1 + 1], &c__1);
+			      work[p] *= cs;
+			      work[q] /= cs;
+			      if (rsvec) {
+				  d__1 = -t * aqoap;
+				  daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
+					  c__1, &v[p * v_dim1 + 1], &c__1);
+				  d__1 = cs * sn * apoaq;
+				  daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
+					  c__1, &v[q * v_dim1 + 1], &c__1);
+			      }
+			  }
+					    } else {
+			  if (work[q] >= 1.) {
+			      d__1 = t * apoaq;
+			      daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
+				      q * a_dim1 + 1], &c__1);
+			      d__1 = -cs * sn * aqoap;
+			      daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
+				      p * a_dim1 + 1], &c__1);
+			      work[p] /= cs;
+			      work[q] *= cs;
+			      if (rsvec) {
+				  d__1 = t * apoaq;
+				  daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
+					  c__1, &v[q * v_dim1 + 1], &c__1);
+				  d__1 = -cs * sn * aqoap;
+				  daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
+					  c__1, &v[p * v_dim1 + 1], &c__1);
+			      }
+			  } else {
+			      if (work[p] >= work[q]) {
+				  d__1 = -t * aqoap;
+				  daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, 
+					  &a[p * a_dim1 + 1], &c__1);
+				  d__1 = cs * sn * apoaq;
+				  daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, 
+					  &a[q * a_dim1 + 1], &c__1);
+				  work[p] *= cs;
+				  work[q] /= cs;
+				  if (rsvec) {
+				      d__1 = -t * aqoap;
+				      daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], 
+					      &c__1, &v[p * v_dim1 + 1], &
+					      c__1);
+				      d__1 = cs * sn * apoaq;
+				      daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], 
+					      &c__1, &v[q * v_dim1 + 1], &
+					      c__1);
+				  }
+			      } else {
+				  d__1 = t * apoaq;
+				  daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, 
+					  &a[q * a_dim1 + 1], &c__1);
+				  d__1 = -cs * sn * aqoap;
+				  daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, 
+					  &a[p * a_dim1 + 1], &c__1);
+				  work[p] /= cs;
+				  work[q] *= cs;
+				  if (rsvec) {
+				      d__1 = t * apoaq;
+				      daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], 
+					      &c__1, &v[q * v_dim1 + 1], &
+					      c__1);
+				      d__1 = -cs * sn * aqoap;
+				      daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], 
+					      &c__1, &v[p * v_dim1 + 1], &
+					      c__1);
+				  }
+			      }
+			  }
+					    }
+					}
+
+				    } else {
+/*              .. have to use modified Gram-Schmidt like transformation */
+					dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
+						work[*n + 1], &c__1);
+					dlascl_("G", &c__0, &c__0, &aapp, &
+						c_b18, m, &c__1, &work[*n + 1]
+, lda, &ierr);
+					dlascl_("G", &c__0, &c__0, &aaqq, &
+						c_b18, m, &c__1, &a[q * 
+						a_dim1 + 1], lda, &ierr);
+					temp1 = -aapq * work[p] / work[q];
+					daxpy_(m, &temp1, &work[*n + 1], &
+						c__1, &a[q * a_dim1 + 1], &
+						c__1);
+					dlascl_("G", &c__0, &c__0, &c_b18, &
+						aaqq, m, &c__1, &a[q * a_dim1 
+						+ 1], lda, &ierr);
+/* Computing MAX */
+					d__1 = 0., d__2 = 1. - aapq * aapq;
+					sva[q] = aaqq * sqrt((max(d__1,d__2)))
+						;
+					mxsinj = max(mxsinj,sfmin);
+				    }
+/*           END IF ROTOK THEN ... ELSE */
+
+/*           In the case of cancellation in updating SVA(q), SVA(p) */
+/*           recompute SVA(q), SVA(p). */
+
+/* Computing 2nd power */
+				    d__1 = sva[q] / aaqq;
+				    if (d__1 * d__1 <= rooteps) {
+					if (aaqq < rootbig && aaqq > 
+						rootsfmin) {
+					    sva[q] = dnrm2_(m, &a[q * a_dim1 
+						    + 1], &c__1) * work[q];
+					} else {
+					    t = 0.;
+					    aaqq = 0.;
+					    dlassq_(m, &a[q * a_dim1 + 1], &
+						    c__1, &t, &aaqq);
+					    sva[q] = t * sqrt(aaqq) * work[q];
+					}
+				    }
+				    if (aapp / aapp0 <= rooteps) {
+					if (aapp < rootbig && aapp > 
+						rootsfmin) {
+					    aapp = dnrm2_(m, &a[p * a_dim1 + 
+						    1], &c__1) * work[p];
+					} else {
+					    t = 0.;
+					    aapp = 0.;
+					    dlassq_(m, &a[p * a_dim1 + 1], &
+						    c__1, &t, &aapp);
+					    aapp = t * sqrt(aapp) * work[p];
+					}
+					sva[p] = aapp;
+				    }
+
+				} else {
+/*        A(:,p) and A(:,q) already numerically orthogonal */
+				    if (ir1 == 0) {
+					++notrot;
+				    }
+/* [RTD]      SKIPPED  = SKIPPED  + 1 */
+				    ++pskipped;
+				}
+			    } else {
+/*        A(:,q) is zero column */
+				if (ir1 == 0) {
+				    ++notrot;
+				}
+				++pskipped;
+			    }
+
+			    if (i__ <= swband && pskipped > rowskip) {
+				if (ir1 == 0) {
+				    aapp = -aapp;
+				}
+				notrot = 0;
+				goto L2103;
+			    }
+
+/* L2002: */
+			}
+/*     END q-LOOP */
+
+L2103:
+/*     bailed out of q-loop */
+
+			sva[p] = aapp;
+
+		    } else {
+			sva[p] = aapp;
+			if (ir1 == 0 && aapp == 0.) {
+/* Computing MIN */
+			    i__4 = igl + kbl - 1;
+			    notrot = notrot + min(i__4,*n) - p;
+			}
+		    }
+
+/* L2001: */
+		}
+/*     end of the p-loop */
+/*     end of doing the block ( ibr, ibr ) */
+/* L1002: */
+	    }
+/*     end of ir1-loop */
+
+/* ... go to the off diagonal blocks */
+
+	    igl = (ibr - 1) * kbl + 1;
+
+	    i__2 = nbl;
+	    for (jbc = ibr + 1; jbc <= i__2; ++jbc) {
+
+		jgl = (jbc - 1) * kbl + 1;
+
+/*        doing the block at ( ibr, jbc ) */
+
+		ijblsk = 0;
+/* Computing MIN */
+		i__4 = igl + kbl - 1;
+		i__3 = min(i__4,*n);
+		for (p = igl; p <= i__3; ++p) {
+
+		    aapp = sva[p];
+		    if (aapp > 0.) {
+
+			pskipped = 0;
+
+/* Computing MIN */
+			i__5 = jgl + kbl - 1;
+			i__4 = min(i__5,*n);
+			for (q = jgl; q <= i__4; ++q) {
+
+			    aaqq = sva[q];
+			    if (aaqq > 0.) {
+				aapp0 = aapp;
+
+/*     -#- M x 2 Jacobi SVD -#- */
+
+/*        Safe Gram matrix computation */
+
+				if (aaqq >= 1.) {
+				    if (aapp >= aaqq) {
+					rotok = small * aapp <= aaqq;
+				    } else {
+					rotok = small * aaqq <= aapp;
+				    }
+				    if (aapp < big / aaqq) {
+					aapq = ddot_(m, &a[p * a_dim1 + 1], &
+						c__1, &a[q * a_dim1 + 1], &
+						c__1) * work[p] * work[q] / 
+						aaqq / aapp;
+				    } else {
+					dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
+						work[*n + 1], &c__1);
+					dlascl_("G", &c__0, &c__0, &aapp, &
+						work[p], m, &c__1, &work[*n + 
+						1], lda, &ierr);
+					aapq = ddot_(m, &work[*n + 1], &c__1, 
+						&a[q * a_dim1 + 1], &c__1) * 
+						work[q] / aaqq;
+				    }
+				} else {
+				    if (aapp >= aaqq) {
+					rotok = aapp <= aaqq / small;
+				    } else {
+					rotok = aaqq <= aapp / small;
+				    }
+				    if (aapp > small / aaqq) {
+					aapq = ddot_(m, &a[p * a_dim1 + 1], &
+						c__1, &a[q * a_dim1 + 1], &
+						c__1) * work[p] * work[q] / 
+						aaqq / aapp;
+				    } else {
+					dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
+						work[*n + 1], &c__1);
+					dlascl_("G", &c__0, &c__0, &aaqq, &
+						work[q], m, &c__1, &work[*n + 
+						1], lda, &ierr);
+					aapq = ddot_(m, &work[*n + 1], &c__1, 
+						&a[p * a_dim1 + 1], &c__1) * 
+						work[p] / aapp;
+				    }
+				}
+
+/* Computing MAX */
+				d__1 = mxaapq, d__2 = abs(aapq);
+				mxaapq = max(d__1,d__2);
+
+/*        TO rotate or NOT to rotate, THAT is the question ... */
+
+				if (abs(aapq) > tol) {
+				    notrot = 0;
+/* [RTD]      ROTATED  = ROTATED + 1 */
+				    pskipped = 0;
+				    ++iswrot;
+
+				    if (rotok) {
+
+					aqoap = aaqq / aapp;
+					apoaq = aapp / aaqq;
+					theta = (d__1 = aqoap - apoaq, abs(
+						d__1)) * -.5 / aapq;
+					if (aaqq > aapp0) {
+					    theta = -theta;
+					}
+
+					if (abs(theta) > bigtheta) {
+					    t = .5 / theta;
+					    fastr[2] = t * work[p] / work[q];
+					    fastr[3] = -t * work[q] / work[p];
+					    drotm_(m, &a[p * a_dim1 + 1], &
+						    c__1, &a[q * a_dim1 + 1], 
+						    &c__1, fastr);
+					    if (rsvec) {
+			  drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * 
+				  v_dim1 + 1], &c__1, fastr);
+					    }
+/* Computing MAX */
+					    d__1 = 0., d__2 = t * apoaq * 
+						    aapq + 1.;
+					    sva[q] = aaqq * sqrt((max(d__1,
+						    d__2)));
+/* Computing MAX */
+					    d__1 = 0., d__2 = 1. - t * aqoap *
+						     aapq;
+					    aapp *= sqrt((max(d__1,d__2)));
+/* Computing MAX */
+					    d__1 = mxsinj, d__2 = abs(t);
+					    mxsinj = max(d__1,d__2);
+					} else {
+
+/*                 .. choose correct signum for THETA and rotate */
+
+					    thsign = -d_sign(&c_b18, &aapq);
+					    if (aaqq > aapp0) {
+			  thsign = -thsign;
+					    }
+					    t = 1. / (theta + thsign * sqrt(
+						    theta * theta + 1.));
+					    cs = sqrt(1. / (t * t + 1.));
+					    sn = t * cs;
+/* Computing MAX */
+					    d__1 = mxsinj, d__2 = abs(sn);
+					    mxsinj = max(d__1,d__2);
+/* Computing MAX */
+					    d__1 = 0., d__2 = t * apoaq * 
+						    aapq + 1.;
+					    sva[q] = aaqq * sqrt((max(d__1,
+						    d__2)));
+					    aapp *= sqrt(1. - t * aqoap * 
+						    aapq);
+
+					    apoaq = work[p] / work[q];
+					    aqoap = work[q] / work[p];
+					    if (work[p] >= 1.) {
+
+			  if (work[q] >= 1.) {
+			      fastr[2] = t * apoaq;
+			      fastr[3] = -t * aqoap;
+			      work[p] *= cs;
+			      work[q] *= cs;
+			      drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q * 
+				      a_dim1 + 1], &c__1, fastr);
+			      if (rsvec) {
+				  drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
+					  q * v_dim1 + 1], &c__1, fastr);
+			      }
+			  } else {
+			      d__1 = -t * aqoap;
+			      daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
+				      p * a_dim1 + 1], &c__1);
+			      d__1 = cs * sn * apoaq;
+			      daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
+				      q * a_dim1 + 1], &c__1);
+			      if (rsvec) {
+				  d__1 = -t * aqoap;
+				  daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
+					  c__1, &v[p * v_dim1 + 1], &c__1);
+				  d__1 = cs * sn * apoaq;
+				  daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
+					  c__1, &v[q * v_dim1 + 1], &c__1);
+			      }
+			      work[p] *= cs;
+			      work[q] /= cs;
+			  }
+					    } else {
+			  if (work[q] >= 1.) {
+			      d__1 = t * apoaq;
+			      daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
+				      q * a_dim1 + 1], &c__1);
+			      d__1 = -cs * sn * aqoap;
+			      daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
+				      p * a_dim1 + 1], &c__1);
+			      if (rsvec) {
+				  d__1 = t * apoaq;
+				  daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
+					  c__1, &v[q * v_dim1 + 1], &c__1);
+				  d__1 = -cs * sn * aqoap;
+				  daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
+					  c__1, &v[p * v_dim1 + 1], &c__1);
+			      }
+			      work[p] /= cs;
+			      work[q] *= cs;
+			  } else {
+			      if (work[p] >= work[q]) {
+				  d__1 = -t * aqoap;
+				  daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, 
+					  &a[p * a_dim1 + 1], &c__1);
+				  d__1 = cs * sn * apoaq;
+				  daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, 
+					  &a[q * a_dim1 + 1], &c__1);
+				  work[p] *= cs;
+				  work[q] /= cs;
+				  if (rsvec) {
+				      d__1 = -t * aqoap;
+				      daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], 
+					      &c__1, &v[p * v_dim1 + 1], &
+					      c__1);
+				      d__1 = cs * sn * apoaq;
+				      daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], 
+					      &c__1, &v[q * v_dim1 + 1], &
+					      c__1);
+				  }
+			      } else {
+				  d__1 = t * apoaq;
+				  daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, 
+					  &a[q * a_dim1 + 1], &c__1);
+				  d__1 = -cs * sn * aqoap;
+				  daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, 
+					  &a[p * a_dim1 + 1], &c__1);
+				  work[p] /= cs;
+				  work[q] *= cs;
+				  if (rsvec) {
+				      d__1 = t * apoaq;
+				      daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], 
+					      &c__1, &v[q * v_dim1 + 1], &
+					      c__1);
+				      d__1 = -cs * sn * aqoap;
+				      daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], 
+					      &c__1, &v[p * v_dim1 + 1], &
+					      c__1);
+				  }
+			      }
+			  }
+					    }
+					}
+
+				    } else {
+					if (aapp > aaqq) {
+					    dcopy_(m, &a[p * a_dim1 + 1], &
+						    c__1, &work[*n + 1], &
+						    c__1);
+					    dlascl_("G", &c__0, &c__0, &aapp, 
+						    &c_b18, m, &c__1, &work[*
+						    n + 1], lda, &ierr);
+					    dlascl_("G", &c__0, &c__0, &aaqq, 
+						    &c_b18, m, &c__1, &a[q * 
+						    a_dim1 + 1], lda, &ierr);
+					    temp1 = -aapq * work[p] / work[q];
+					    daxpy_(m, &temp1, &work[*n + 1], &
+						    c__1, &a[q * a_dim1 + 1], 
+						    &c__1);
+					    dlascl_("G", &c__0, &c__0, &c_b18, 
+						     &aaqq, m, &c__1, &a[q * 
+						    a_dim1 + 1], lda, &ierr);
+/* Computing MAX */
+					    d__1 = 0., d__2 = 1. - aapq * 
+						    aapq;
+					    sva[q] = aaqq * sqrt((max(d__1,
+						    d__2)));
+					    mxsinj = max(mxsinj,sfmin);
+					} else {
+					    dcopy_(m, &a[q * a_dim1 + 1], &
+						    c__1, &work[*n + 1], &
+						    c__1);
+					    dlascl_("G", &c__0, &c__0, &aaqq, 
+						    &c_b18, m, &c__1, &work[*
+						    n + 1], lda, &ierr);
+					    dlascl_("G", &c__0, &c__0, &aapp, 
+						    &c_b18, m, &c__1, &a[p * 
+						    a_dim1 + 1], lda, &ierr);
+					    temp1 = -aapq * work[q] / work[p];
+					    daxpy_(m, &temp1, &work[*n + 1], &
+						    c__1, &a[p * a_dim1 + 1], 
+						    &c__1);
+					    dlascl_("G", &c__0, &c__0, &c_b18, 
+						     &aapp, m, &c__1, &a[p * 
+						    a_dim1 + 1], lda, &ierr);
+/* Computing MAX */
+					    d__1 = 0., d__2 = 1. - aapq * 
+						    aapq;
+					    sva[p] = aapp * sqrt((max(d__1,
+						    d__2)));
+					    mxsinj = max(mxsinj,sfmin);
+					}
+				    }
+/*           END IF ROTOK THEN ... ELSE */
+
+/*           In the case of cancellation in updating SVA(q) */
+/*           .. recompute SVA(q) */
+/* Computing 2nd power */
+				    d__1 = sva[q] / aaqq;
+				    if (d__1 * d__1 <= rooteps) {
+					if (aaqq < rootbig && aaqq > 
+						rootsfmin) {
+					    sva[q] = dnrm2_(m, &a[q * a_dim1 
+						    + 1], &c__1) * work[q];
+					} else {
+					    t = 0.;
+					    aaqq = 0.;
+					    dlassq_(m, &a[q * a_dim1 + 1], &
+						    c__1, &t, &aaqq);
+					    sva[q] = t * sqrt(aaqq) * work[q];
+					}
+				    }
+/* Computing 2nd power */
+				    d__1 = aapp / aapp0;
+				    if (d__1 * d__1 <= rooteps) {
+					if (aapp < rootbig && aapp > 
+						rootsfmin) {
+					    aapp = dnrm2_(m, &a[p * a_dim1 + 
+						    1], &c__1) * work[p];
+					} else {
+					    t = 0.;
+					    aapp = 0.;
+					    dlassq_(m, &a[p * a_dim1 + 1], &
+						    c__1, &t, &aapp);
+					    aapp = t * sqrt(aapp) * work[p];
+					}
+					sva[p] = aapp;
+				    }
+/*              end of OK rotation */
+				} else {
+				    ++notrot;
+/* [RTD]      SKIPPED  = SKIPPED  + 1 */
+				    ++pskipped;
+				    ++ijblsk;
+				}
+			    } else {
+				++notrot;
+				++pskipped;
+				++ijblsk;
+			    }
+
+			    if (i__ <= swband && ijblsk >= blskip) {
+				sva[p] = aapp;
+				notrot = 0;
+				goto L2011;
+			    }
+			    if (i__ <= swband && pskipped > rowskip) {
+				aapp = -aapp;
+				notrot = 0;
+				goto L2203;
+			    }
+
+/* L2200: */
+			}
+/*        end of the q-loop */
+L2203:
+
+			sva[p] = aapp;
+
+		    } else {
+
+			if (aapp == 0.) {
+/* Computing MIN */
+			    i__4 = jgl + kbl - 1;
+			    notrot = notrot + min(i__4,*n) - jgl + 1;
+			}
+			if (aapp < 0.) {
+			    notrot = 0;
+			}
+
+		    }
+
+/* L2100: */
+		}
+/*     end of the p-loop */
+/* L2010: */
+	    }
+/*     end of the jbc-loop */
+L2011:
+/* 2011 bailed out of the jbc-loop */
+/* Computing MIN */
+	    i__3 = igl + kbl - 1;
+	    i__2 = min(i__3,*n);
+	    for (p = igl; p <= i__2; ++p) {
+		sva[p] = (d__1 = sva[p], abs(d__1));
+/* L2012: */
+	    }
+/* ** */
+/* L2000: */
+	}
+/* 2000 :: end of the ibr-loop */
+
+/*     .. update SVA(N) */
+	if (sva[*n] < rootbig && sva[*n] > rootsfmin) {
+	    sva[*n] = dnrm2_(m, &a[*n * a_dim1 + 1], &c__1) * work[*n];
+	} else {
+	    t = 0.;
+	    aapp = 0.;
+	    dlassq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
+	    sva[*n] = t * sqrt(aapp) * work[*n];
+	}
+
+/*     Additional steering devices */
+
+	if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
+	    swband = i__;
+	}
+
+	if (i__ > swband + 1 && mxaapq < sqrt((doublereal) (*n)) * tol && (
+		doublereal) (*n) * mxaapq * mxsinj < tol) {
+	    goto L1994;
+	}
+
+	if (notrot >= emptsw) {
+	    goto L1994;
+	}
+
+/* L1993: */
+    }
+/*     end i=1:NSWEEP loop */
+
+/* #:( Reaching this point means that the procedure has not converged. */
+    *info = 29;
+    goto L1995;
+
+L1994:
+/* #:) Reaching this point means numerical convergence after the i-th */
+/*     sweep. */
+
+    *info = 0;
+/* #:) INFO = 0 confirms successful iterations. */
+L1995:
+
+/*     Sort the singular values and find how many are above */
+/*     the underflow threshold. */
+
+    n2 = 0;
+    n4 = 0;
+    i__1 = *n - 1;
+    for (p = 1; p <= i__1; ++p) {
+	i__2 = *n - p + 1;
+	q = idamax_(&i__2, &sva[p], &c__1) + p - 1;
+	if (p != q) {
+	    temp1 = sva[p];
+	    sva[p] = sva[q];
+	    sva[q] = temp1;
+	    temp1 = work[p];
+	    work[p] = work[q];
+	    work[q] = temp1;
+	    dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1);
+	    if (rsvec) {
+		dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &
+			c__1);
+	    }
+	}
+	if (sva[p] != 0.) {
+	    ++n4;
+	    if (sva[p] * scale > sfmin) {
+		++n2;
+	    }
+	}
+/* L5991: */
+    }
+    if (sva[*n] != 0.) {
+	++n4;
+	if (sva[*n] * scale > sfmin) {
+	    ++n2;
+	}
+    }
+
+/*     Normalize the left singular vectors. */
+
+    if (lsvec || uctol) {
+	i__1 = n2;
+	for (p = 1; p <= i__1; ++p) {
+	    d__1 = work[p] / sva[p];
+	    dscal_(m, &d__1, &a[p * a_dim1 + 1], &c__1);
+/* L1998: */
+	}
+    }
+
+/*     Scale the product of Jacobi rotations (assemble the fast rotations). */
+
+    if (rsvec) {
+	if (applv) {
+	    i__1 = *n;
+	    for (p = 1; p <= i__1; ++p) {
+		dscal_(&mvl, &work[p], &v[p * v_dim1 + 1], &c__1);
+/* L2398: */
+	    }
+	} else {
+	    i__1 = *n;
+	    for (p = 1; p <= i__1; ++p) {
+		temp1 = 1. / dnrm2_(&mvl, &v[p * v_dim1 + 1], &c__1);
+		dscal_(&mvl, &temp1, &v[p * v_dim1 + 1], &c__1);
+/* L2399: */
+	    }
+	}
+    }
+
+/*     Undo scaling, if necessary (and possible). */
+    if (scale > 1. && sva[1] < big / scale || scale < 1. && sva[n2] > sfmin / 
+	    scale) {
+	i__1 = *n;
+	for (p = 1; p <= i__1; ++p) {
+	    sva[p] = scale * sva[p];
+/* L2400: */
+	}
+	scale = 1.;
+    }
+
+    work[1] = scale;
+/*     The singular values of A are SCALE*SVA(1:N). If SCALE.NE.ONE */
+/*     then some of the singular values may overflow or underflow and */
+/*     the spectrum is given in this factored representation. */
+
+    work[2] = (doublereal) n4;
+/*     N4 is the number of computed nonzero singular values of A. */
+
+    work[3] = (doublereal) n2;
+/*     N2 is the number of singular values of A greater than SFMIN. */
+/*     If N2<N, SVA(N2:N) contains ZEROS and/or denormalized numbers */
+/*     that may carry some information. */
+
+    work[4] = (doublereal) i__;
+/*     i is the index of the last sweep before declaring convergence. */
+
+    work[5] = mxaapq;
+/*     MXAAPQ is the largest absolute value of scaled pivots in the */
+/*     last sweep */
+
+    work[6] = mxsinj;
+/*     MXSINJ is the largest absolute value of the sines of Jacobi angles */
+/*     in the last sweep */
+
+    return 0;
+/*     .. */
+/*     .. END OF DGESVJ */
+/*     .. */
+} /* dgesvj_ */